Cryptology ePrint Archive: Report 2018/482

Abstract: Most multi-party computation protocols allow secure computation of arithmetic circuits over a finite field, such as the integers modulo a prime.
In the more natural setting of integer computations modulo $2^{k}$, which are useful for simplifying implementations and applications, no solutions with active security are known unless the majority of the participants are honest.

We present a new scheme for information-theoretic MACs that are homomorphic modulo $2^k$, and are as efficient as the well-known standard solutions that are homomorphic over fields.
We apply this to construct an MPC protocol for dishonest majority in the preprocessing model that has efficiency comparable to the well-known SPDZ protocol (Damgård et al., CRYPTO 2012), with operations modulo $2^k$ instead of over a field.
We also construct a matching preprocessing protocol based on oblivious transfer, which is in the style of the MASCOT protocol (Keller et al., CCS 2016) and almost as efficient.